**High School Number Sense Lesson 6: Converting Fractions to Decimals**

Historically, this specific type of conversion problem only shows up a few times per year. But since it did show up 5 times on high school tests this year, it's important that we cover it now. This year this concept showed up most often as question # 6.

To convert a fraction to a decimal, we first consider the fact that the word

**decimal**revers to our

**base 10**system. I personally look at each denominator and think "how many times does that number go into 10?" More often, I have to determine how many times the denominator goes into 100. With these problems, we're essentially inventing a fraction and then "un-reducing" it so it ends up as a decimal. This is easier demonstrated than explained, so here goes:

**Number Dojo Level: 22**

**The Old Way (Long Division): 4/5 = ___ decimal**

- Divide the numerator by the denominator. 5 goes into 4 zero times. Use a decimal and add a zero.
- 5 goes into 40 eight times, but with one decimal point.
- The answer is
**.8**

The New Way (Using Logic): 4/5 = ___ decimal

The New Way (Using Logic): 4/5 = ___ decimal

- Figure out how many times the denominator goes into 100. 5 goes into 100,
**20**times. - Multiply the numerator by that number, and then divide by 100. 4 x 20 =
**80**; 80 ÷ 100 =**.8**

**Example 1: 11/20 = ___ decimal**

- 20 goes into 100,
**5**times. - 11 x 5 =
**55**. 55 ÷ 100 =**.55**

**Example 2: 7/4 = ___ decimal**

- 4 goes into 100,
**25**times. - 7 x 25 =
**175**. 175 ÷ 100 =**1.75**

**Example 3: 5/8 = ___ decimal**

****8 goes into 100,**12.5**times.- 5 x 12.5 =
**62.5**. 62.5 ÷ 100 =**.625**

**Example 4: 9/16 = ___ decimal**

- 16 goes into 100,
**6.25**times. - 9 x 6.25 =
**56.25**. 56.25 ÷ 100 =**.5625**

**Notes:**

- Examples 3 & 4 may have been a bit of a stretch. I highly recommend that my students download the flashcards (found on the Worksheets page). These flashcards help students memorize their decimal equivalents to fractions with denominators up to 16.
- Without having to memorize every fraction with denominator 8 or 16, it may be easier to realize that since 1/4 = .25, then 1/8 = .125 (half of .25), and 1/16 = .0625 (half of .125). Then for fractions like 5/8, realize that it is the same as 4/8 + 1/8, which is .5 + .125, which equals .625. For 9/16, realize it is 8/16 + 1/16, which is .5 + .0625, which equals .5625.

**Here's a free worksheet to help you practice ConvFracDeci:**

convfracdeci.pdf |

**Up Next for High School: OrderOfOper**